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Machine learning in spectral domain

delete2021-02-26
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OA
AI
L
Lorenzo Giambagli
L
Lorenzo Buffoni
T
Timotéo Carletti
N
Nocentini, Walter
F
Fanelli, Duccio *
DOI:10.1038/s41467-021-21481-0delete
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摘要

摘要

En 中文
Deep neural networks are usually trained in the space of the nodes, by adjusting the weights of existing links via suitable optimization protocols. We here propose a radically new approach which anchors the learning process to reciprocal space. Specifically, the training acts on the spectral domain and seeks to modify the eigenvalues and eigenvectors of transfer operators in direct space. The proposed method is ductile and can be tailored to return either linear or non-linear classifiers. Adjusting the eigenvalues, when freezing the eigenvectors entries, yields performances that are superior to those attained with standard methods restricted to operate with an identical number of free parameters. To recover a feed-forward architecture in direct space, we have postulated a nested indentation of the eigenvectors. Different non-orthogonal basis could be employed to export the spectral learning to other frameworks, as e.g. reservoir computing. Theoretical aspects of automated learning from data involving deep neural networks have open questions. Here Giambagli et al. show that training the neural networks in the spectral domain of the network coupling matrices can reduce the amount of learning parameters and improve the pre-training process.
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Nature Communications 封面图
Nature Communications
IF:
15.7
论文数:
9.4W
被引数:
91.2W

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U
university of florence
学者数:
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论文数: 3.1W
被引数: 42
U
University of Namur
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论文数: 2.3K
被引数: 3.3K
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